This page covers Statistics at the College Freshman level, delivered as a formula cheat sheet. Descriptive statistics, probability distributions, hypothesis testing, and regression. The most-used. The material here corresponds to First year of university courses: Calculus 1 and Calculus 2.
The key formulas for Statistics at the College Freshman level are organised below. Each formula is accompanied by a note on when it applies and what common variations exist.
The skills covered by these formulas are: Descriptive statistics, Normal distribution, Hypothesis testing, Confidence intervals, Linear regression.
For each formula, read the conditions carefully. Many errors in Statistics come from applying a formula outside its domain of validity — using a geometric formula that assumes a right angle when the angle is not specified, or applying a probability rule that requires independence when the events are dependent.
Use this sheet as a revision tool after you have worked through problems — not as a first introduction to the material. A formula you have derived or used is one you will remember; a formula you have only read is one you will forget under exam pressure.
Worked Example
A standard statistics problem at the college freshman level.
Work through step by step: identify what is given, what is asked, apply the relevant technique, and check your answer against the original conditions.
Interpreting a p-value as the probability the null hypothesis is true. A p-value is the probability of observing the data (or more extreme) assuming the null is true — a very different claim.
Frequently Asked Questions
How is Statistics different at the College 1st Year level compared to earlier levels?
At the College Freshman level, Statistics builds on First year of university prerequisites. Students are expected to have completed Calculus 1 before tackling this material.
Which exams test Statistics at this level?
AP Statistics, GRE, Social science research methods.
What is the single most effective way to practise Statistics for College 1st Year students?
The most effective practice at the College Freshman level is deliberate work on novel problem setups — not repeated drilling of the same template. Attempt problems before looking at solutions, and review errors by identifying the specific step where the reasoning broke down.